Question

A pole of 8m high is fixed on the top of a tower. The angle of the top of the pole observed
from a point A on the ground is 45° and the angle of depression of the point 'A' from the top
of the tower is 45°. The height of the tower and distance of point to A to the top of pole
respectively is.​

Answer 1

Answer:

45 + 45 is the addition ok

Answer 2

10.95 and 10.95

Step-by-step explanation:

Let the height of tower be X

Height of pole is 8m

Let the distance between tower and point A be the 'Base'.

Angle of elevation from point A to top of pole is 60

Angle of depression from top of tower to point A is 45

Then,

$tan 45 = \frac{X}{base}\\ \\1 = \frac{X}{base}\\ \\Base = X$

$tan 60 = \frac{8+X}{Base}\\ \\\sqrt{3} = \frac{8+X}{X}\\ \\X\sqrt{3} = 8+X\\\\1.73X = 8+X\\\\0.73X = 8\\\\X = \frac{8}{0.73} \\\\X = 10.95$

Therefore, the height of tower is 10.95m and the distance between tower and point A is 10.95m